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WASHINGTON (CNN) -- Shortly after 9/11, al Qaeda began planning to use shoe bombers to hijack a commercial airplane and fly it into the tallest building in Los Angeles, California, President Bush said Thursday.

The details were the first from the administration about the West Coast airliner plot, which was thwarted in 2002 and initially disclosed by the White House last year.

The plot was set in motion by Khalid Shaikh Mohammed, the alleged mastermind of the September 11, 2001, attacks, a month after the airplanes crashed into the World Trade Center and Pentagon, Bush said. It involved terrorists from al Qaeda's Southeast Asia wing, Jemaah Islamiyah. (Watch Bush's disclosure on the timing and location -- 1:45)

"Rather than use Arab hijackers, Khalid Shaikh Mohammed sought out young men from Southeast Asia whom he believed would not arouse as much suspicion," Bush said.

Mohammed was captured in Pakistan in 2003.

Bush said the plotters planned to use shoe bombs to breach the cockpit door and hijack the plane.

At a later briefing, Bush's homeland security adviser, Fran Townsend, said the leader of the four-man cell that was planning the attack had been arrested in 2003.

She did not identify him, but said he was trained personally by Mohammed "in the shoe bomb technique."

"You'll all recall that there was the arrest of the shoe bomber Richard Reid in December of 2001, and he was instructing the cell leader on the use of the same technique," Townsend said, but later added it was not clear if Reid was directly involved in the Los Angeles plot.

Reid pleaded guilty in 2002 to trying to blow up a trans-Atlantic airplane with explosives he had hidden in his shoes. Intelligence indicated Reid reported to Mohammed.

U.S. authorities don't have details on the West Coast plot, such as whether a specific flight was targeted or a day scheduled, Townsend said.

She added that the hijacking was intended to be part of the 9/11 attacks, but Osama bin Laden instructed the terrorists to focus solely on the East Coast that day.

"It's our understanding now that it was too difficult to get enough operatives for both the East and West Coast plots at the same time," she said.

Al Qaeda's Southeast Asia leader, known as Hambali, had recruited Jemaah Islamiyah operatives for the plot, Bush said. Hambali was arrested in 2003 in Thailand, five months after Mohammed was arrested in Pakistan.

The would-be hijackers met with al Qaeda leader Osama bin Laden and then began preparing for the attack, which was derailed in early 2002, Bush said.

The purported plot was one of 10 on a list first released by the White House in October. (Full story)

The intended target of the attack was a building then known as the Library Tower. It was renamed the U.S. Bank Tower in 2003 and, at 1,018 feet, is the tallest building west of the Mississippi River. It is among the 25 tallest buildings in the world.

Bush credited international cooperation in the war on terrorism with saving American lives.

"The West Coast plot shows we face a relentless and determined enemy that requires unprecedented cooperation from other nations," he said. "By working together, we stopped a catastrophic attack."

Two members of the Senate Intelligence Committee, Sens. Jay Rockefeller, D-West Virginia, and Dianne Feinstein, D-California, questioned the timing and the details of Bush's revelation.

"It may be that they're tired of talking about the Brooklyn Bridge, and they're trying to find a different edifice of some sort," Rockefeller said.

Added Feinstein, "All I'm saying is that's not a new revelation and I've never seen anything that indicated whether the second wave was bona fide or not."

Emphasizing that there is no imminent threat to his city, Los Angeles Mayor Antonio Villaraigosa said during a Thursday news conference that he had already heard about the 2002 threat, but Thursday was the first time he'd learned the details. (Watch the mayor discuss the threat of terror -- 4:36)

"The city of Los Angeles has implemented significant security measures since that time," the mayor said, explaining that security personnel at high-rise buildings throughout the city have received training in terrorism detection, evacuations and diminishing the impact of an explosion.